In-situ graph reasoning and knowledge expansion using Graph-PReFLexOR, a class of graph-native reasoning models

In-situ graph reasoning and knowledge expansion are important elements in the advancement of automated systems for scientific discovery. This work introduces Graph-PReFLexOR (Graph-based Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning), a generative framework designed to perform dynamic graph reasoning and iteratively expand domain knowledge. Graph-PReFLexOR is trained inspired by reinforcement learning methods, and leverages construct detailed knowledge graphs and abstract representations, enabling hierarchical reasoning and adaptive learning, to achieve in-situ graph generation, symbolic representation of arguments and logical deduction, to ultimately formulate a response to tasks. Critically, Graph-PReFLexOR formalizes reasoning as a structured mapping. Inspired by category theory modeling that emphasizes how objects relate, rather than their internal detail, the graph encodes concepts as nodes and relationships as directed edges.

By combining in -situ symbolic and contextual inference, the framework generates its own structured representation on the fly and thereby captures complex interdependencies and translates them into domain-specific interpretable insights. Demonstrations include generating and expanding scientific hypotheses and fabricating dynamic transformations in graph topologies, with applications in materials science and engineering, and multi-disciplinary relationship discovery.

For instance, Graph-PReFLexOR demonstrates creative reasoning by generating poetic representations that blend abstract concepts like `thin places'--mythological notions of blurred boundaries--into scientific frameworks such as protein biomaterials engineering. Through its knowledge garden growth strategy, the model dynamically integrates insights from diverse domains, enabling the discovery of profound interdisciplinary connections that link art, philosophy, and science.

Figure 1: Overview of the approach used in this paper, presenting The concept of multi-step reflection (panel a), graph-based modeling of context and tasks (panel b), abstract pattern formulation (panel c), and finally, integrated in the multi-stage reasoning mechanisms (panel d).

Graph reasoning examples

Figure 2: Visualization of the integrated knowledge graph based on the graph reasoning strategy invoking knowledge expansion. The data is organized here effectively as an integrated graph rather than by prompt, and laid out using the Fruchterman Reingold layout algorithm. Panel a, node size by node degree. Panel b, node size by page rank. Panel c, node size by bridging coefficient. Panel d, node size by domain prestige (metric defined by fraction of nodes within a network that are directly od indirectly pointing to it).

Knowledge garden algorithm

Figure 3: Grown knowledge graph based on the prompt Discuss protein design based on collagen and elastin. Here, the agentic system is specifically charged to develop new questions that integrate dissimilar fields such as philosophy or art. The visualization depicts nodes sized and colored by page rank, with top nodes being Biolumniscent Biomaterial (most significant node also per node degree), Protein, Installation, Elastin and Concept. A unique feature is the incorporation of the concept of thin places, a concept drawn from various mythological and spiritual traditions that invokes sites or moments where the boundary between the physical world and a transcendent realm is perceived to be exceptionally thin or permeable. The model identifies this as an interesting association for this particular task, which is particularly interesting as a way to create a new concept that incorporates highly multidisciplinary relationships.

Reference

@article{buehler2025GraphPRefLexOR,
      title={In-situ graph reasoning and knowledge expansion using Graph-PReFLexOR}, 
      author={Markus J. Buehler},
      year={2025},
      eprint={2501.08120},
      archivePrefix={arXiv},
      primaryClass={cs.AI},
      url={https://arxiv.org/abs/2501.08120}, 
}